Question

The median of following series $520,20,340,190,35,800,1210,50,80$
A. $1210$
B. $520$
C. $190$
D. None of these.

Answer 1

Hint: To find the median of given data we need to arrange the given data in ascending or descending order. We know that the Median is the Mid term of the arranged data. So, we will cancel the one term on right side and other term on left side at a time. We will keep on doing like this until we will get one value. If we get one value then that value is the Median of the data. If we get two numbers at last, then we will declare the mean/average of those two numbers as the Median.

Complete step by step answer:
Given data,
$520,20,340,190,35,800,1210,50,80$
Arranging the above data from smaller to larger elements. i.e. the ascending order of the above data is given by
\[\text{20,35,50,80,190,340,520,800,1210}\]
The number of elements in the given data is $9$.
Eliminating the rightmost element$\left( 1210 \right)$ and leftmost element$\left( 20 \right)$ from the arrangement, then we will get
\[35,50,80,190,340,520,800\]
Again, Eliminating the rightmost element$\left( 800 \right)$ and leftmost element$\left( 35 \right)$ from the arrangement, then we will get
\[50,80,190,340,520\]
Again, Eliminating the rightmost element$\left( 520 \right)$ and leftmost element$\left( 50 \right)$ from the arrangement, then we will get
\[80,190,340\]
Again, Eliminating the rightmost element$\left( 340 \right)$ and leftmost element$\left( 80 \right)$ from the arrangement, then we will get
\[190\]

So, the correct answer is “Option C”.

Note: we can also get the same answer when we arranged the given data in descending order.
The descending order of the arrangement is
\[\text{1210,800,520,340,190,80,50,35,20}\]
For the above arrangement the eliminated terms are
${{1}^{st}}$eliminated $\to 120,20$
${{2}^{nd}}$eliminated $\to 800,35$
${{3}^{rd}}$ eliminated $\to 520,50$
${{4}^{th}}$ eliminated $\to 340,80$
The remaining element is $190$. Hence the mean of the data is $190$.
Hence from both the arrangements we got the same answer.